In the above diagram, two indifference curves are showing cutting each other at point B. The curves will lie very close to one another and may even become indistinguishable from one another. Here we assume utility functions to be twice continuously differentiable. The following are those properties: Indifference curves are infinite Sample pictures of indifference curves may show you one or two indifference curves. This violates the basic assumption of indifference curves.
Such a situation is encountered when two commodities are perfect complements, so that they are consumed in fixed proportions. We can clearly see that the rate of decrease in consumption of coffee is not the same as rate of increase in consumption of cigarette. This violates the basic definition of an indifference curve. The better substitutes the two goods are for each other, the closer the indifference curve approaches to the straight-line so that when the two goods are perfect substitutes, the indifference curve is a straight line. But point С which lies on both the curves yields the same level of satisfaction as point A and B. Further, the indifference curves have no width and every point in the commodity space has indifference curve through it. In reality, commodities are not perfect substitutes or perfect complements to each other.
Let us look at the following figure 1. An indifference curve is the locus of all the points, representing different combinations, that are equally satisfactory to the consumer. Thus, averages are preferred to extremes. He is not supposed to purchase only one commodity. The better sets for points X, Y and Z, respectively are convex but none is strictly convex. Table: Indifference schedule Combination Mangoes Oranges A 1 14 B 2 9 C 3 6 D 4 4 E 5 2. Such a situation is encountered when the difference in utility between two points Y and X is so small that even a rational consumer cannot perceive it, i.
When he started consuming two cigarettes a day, his coffee consumption dropped to 8 cups a day. Straight-line indifference curves of perfect substitutes are shown m Fig. It is exhibited by fig. Thus an indifference curve slopes downward. Indifference curves can never intersect each other: As two indifference curves cannot represent the same level of satisfaction, they cannot intersect each other. Since any combination of the two goods on an indifference curve gives equal level of satisfaction, the consumer is indifferent to any combination he consumes.
Satiation in One Commodity : If the consumer reaches satiation in respect of one commodity, the indifference curve will have upward sloping segments like the one shown in Fig. Here X dominates Y, as does Z. So we may now examine what kind of preferences give rise what shapes of indifference curves. . Other Possibilities Suppose that indifference curve is not convex to the origin.
Learning Goal 3: Understand the relevance of ordinal approach to consumer behaviour. Finally, an increase in the standard deviation from 0. Therefore, the rate of decrease in a commodity cannot be equal to the rate of increase in another commodity. Only a convex indifference curve can mean a diminishing marginal rate of substitution of X for K If indifference curve was concave to the origin it would imply that the marginal rate of substitution of X for y increased as more and more of X was substituted, for Y. Volker Böhm and Hans Haller 1987. If indifference curves were concave or straight lines, the consumer would succumb to monomania, that is, he would buy and consume only one good. As we know that all indifference curve slope downward to right or they have negative slopes.
The numbers can be in the ascending order of 1, 2, 4, 6 or 1, 2, 3, 4, etc. Therefore the total satisfaction increases. In other words, the combinations which lie on a higher indifference curve will be preferred to the combinations which lie on a lower indifference curve. The combination of goods which lies on a higher indifference curve will be preferred by a consumer to the combination which lies on a lower indifference curve. In fact, any point in the shaded area with Y as origin dominates Y. Yet no utility function exists that represents this preference ordering. In this case, ΔY 2 is greater than ΔY 1, ΔY 3 is greater than ΔY 2, and so on.
Figure 6 a shows an indifference curve that is concave to the origin. To prove this property, let us take indifference curves contrary to this assumption. Concluding Comments : As a result of these axioms, we can represent the preference ordering of the consumer by a set of continuous convex-to-the-origin indifference curves, such that each consumption bundle lies on one and only one of them. The axiom of transitivity, therefore, implies that X ~ Y. These two indifference curves represent two different levels of satisfaction.
Thus, the best consumption bundle open to a consumer is the one lying on the highest possible attainable indifference curve. The table given below is an example of indifference schedule and the graph that follows is the illustration of that schedule. And, indifference curve theory assumes that the consumer has not reached the point of satiety. But the consumer wanted to buy two commodities. According to diminishing marginal rate of substitution, the rate of substitution of commodity X for Y decreases more and more with each successive substitution of X for Y.
The better substitutes the two goods are for each other, the closer the indifference curve approaches to the straight line so that when the two goods are perfect substitutes the indifference curve is a straight line. Definitions of Indifference Curve Prof. Thus indifference curve is steeper towards the Y axis and gradual towards the X axis. This means that an indifference curve has to lie consistently above or below another. At the extreme, when two goods cannot at all be substituted for each other, that is, when the two goods are perfect complementary goods, as for example gasoline and coolant in a car, the indifference curve will consist of two straight lines with a right angle bent which is convex to the origin as shown in Fig.